Maps have distortion because it is mathematically impossible to perfectly represent a three-dimensional sphere (the Earth) on a two-dimensional flat surface (a map) without altering some of its properties.
The Impossibility of Perfect Projection
Imagine trying to flatten an orange peel without tearing or stretching it. You'll inevitably end up with gaps or distortions. This analogy illustrates the fundamental problem of mapmaking. Carl Frederick Gauss, a prominent mathematician, proved this impossibility in 1828.
Types of Distortion
Since distortion is unavoidable, mapmakers choose to preserve certain properties at the expense of others. The four main properties that maps can distort are:
- Shape: The shapes of landmasses and countries can be altered.
- Area: The relative sizes of areas can be misrepresented.
- Distance: The distances between points can be inaccurate.
- Direction: The angles and directions between locations can be skewed.
Map Projections and Their Trade-offs
Different map projections prioritize different properties, leading to various types of distortion:
| Projection Type | Properties Preserved | Properties Distorted | Examples |
|---|---|---|---|
| Conformal | Shape (locally) | Area | Mercator Projection |
| Equal Area | Area | Shape, Angles | Gall-Peters Projection, Goode homolosine |
| Equidistant | Distance (from a point) | Other properties | Azimuthal Equidistant |
| Compromise | Tries to balance all | All properties, slightly | Robinson Projection |
- Conformal projections, like the Mercator projection, accurately represent the shapes of small areas, but significantly distort the size of landmasses, especially at higher latitudes. This is why Greenland appears much larger than it actually is compared to Africa.
- Equal-area projections, such as the Gall-Peters projection, accurately represent the relative sizes of areas, but distort the shapes of landmasses.
- Equidistant projections accurately represent distances from a single designated point to all other points on the map. However, distance accuracy to other points from locations that are not the central point will be distorted.
- Compromise projections, like the Robinson projection, attempt to minimize all types of distortion, but don't perfectly preserve any single property. They're often used for general-purpose maps.
Conclusion
The inherent challenge of representing a sphere on a flat plane necessitates distortion in maps. Mapmakers choose different projections based on the intended purpose of the map, prioritizing the preservation of specific properties while accepting the inevitable distortions in others.
